#thematic

There is no philosophy which is not founded upon knowledge of the phenomena, but to get any profit from this knowledge it is absolutely necessary to be a mathematician. ↗

— Daniel Bernoulli

#any #founded #get #knowledge #mathematician

Mathematical discoveries, like springtime violets in the woods, have their season which no man can hasten or retard. ↗

— Janos Bolyai

#hasten #like #man #mathematical #retard

No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful. ↗

— George Boole

#also #appear #beautiful #being #being beautiful

In mathematics the art of proposing a question must be held of higher value than solving it. ↗

— Georg Cantor

#held #higher #mathematics #must #proposing

I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers. ↗

— Georg Cantor

#concerning #defended #frequently #held #i

The only thing that might have annoyed some mathematicians was the presumption of assuming that maybe the axiom of choice could fail, and that we should look into contrary assumptions. ↗

— Alonzo Church

#assuming #assumptions #axiom #choice #contrary

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. ↗

— Richard Courant

#aesthetic #analysis #basic #basic elements #construction

The problem is that no ethical system has ever achieved consensus. Ethical systems are completely unlike mathematics or science. This is a source of concern. ↗

— Daniel Dennett

#completely #concern #consensus #ethical #ever

Proof is an idol before whom the pure mathematician tortures himself. ↗

— Arthur Eddington

#himself #idol #mathematician #proof #pure

My beautiful proof lies all in ruins. ↗

— Georg Cantor

#ruins #beauty